TRENTON — State Senate President Stephen Sweeney and Jersey City Mayor Steve Fulop have reached an agreement on a bill to trim the city's pension system.

Sweeney has scheduled a hearing on a bill, but with an amendment. Under the new version, all the money Jersey City saves from reducing certain expenses would go back into the city’s underfunded pension system – not its general budget.

"This pension is the unhealthiest in the state," Sweeney said. "I can’t see taking money away from the pension, or away from the retirees, and then putting it in the budget. That’s not right."

In a statement, Fulop said he's OK with the changes.

"This bill should never have seen this much drama in Trenton as it was a non-controversial bill that received unanimous bipartisan support in the Assembly," he said. "We are glad to see it moving forward and the current form works well for all parties."

The bill will be heard at a Senate Budget Committee meeting that was just scheduled for Monday morning. If approved, the full state Senate would vote on it later in the day.

Sweeney and Fulop have butted heads over the legislation, which passed the Assembly by a vote of 79-0 last month. The two men are widely considered potential rivals for governor in 2017, and Fulop accused Sweeney of playing political games while harming Jersey City residents.

"The only reason someone wouldn't support it is because they want to punish Jersey City," Fulop said Monday.

A Sweeney spokesman shot back that "instead of focusing on politics for the last six months, (Fulop) should have been focusing on his job for the taxpayers of Jersey City."

Fulop, who pushed for the bill, estimated it would save Jersey City anywhere from $12 million to $20 million over eight years. But Sweeney’s amendment would mean the bulk of those savings – achieved by reducing current and future retirees’ annual cost of living adjustments – would be devoted to the pension system and unavailable to Fulop for other purposes.

Fulop raised taxes 7.6 percent shortly just days after he took office in July and blamed it on his predecessor, Jerramiah Healy.

Jersey City is the only municipality in the state with its own pension system. According to the Office of Legislative Services, it is 41.9 percent funded.

Under the bill (A4536), cost of living adjustments for adjustments for retirees would be reduced from 100 percent of the Consumer Price Index to 50 percent.

It also trims benefits in several other ways, including raising the city’s retirement age for new employees from 60 to 65, requiring them to have 25 years of service instead of 20 years, and increasing the amount of time before they are eligible to retire early to 30 years from 25 years.

Sweeney later issued a joint statement with the bill's three sponsors: Assembly Speaker-Elect Vincent Prieto (D-Hudson) and state Sens. Sandra Cunningham (D-Hudson) and Brian Stack (D-Hudson).

"This will not only protect the hard working men and women of Jersey City, but will guarantee that the savings are used solely to improve the solvency of the pension system," it reads. "Our collective goal remains doing what is best for Jersey City and this amended legislation does just that."